Question: A stretch of highway that is $12\dfrac14$ kilometers long has speed limit signs every $\dfrac78$ of a kilometer. How many speed limit signs are on this stretch of highway?
We can think about this problem like this: $ {\text{number of signs}} = {\text{length of highway}} \div {\text{distance between signs}}$ ${\text{?}} = {12\dfrac14 \text{ kilometers}} \div {\dfrac{7}{8} \text{ kilometer}}$ $\phantom{?} = {\dfrac{49}{4} \text{ km}} \div {\dfrac{7}{8} \text{ km}} ~~~~~~~{\text{Rewrite } {12\dfrac14} \text{ as } { \dfrac{49}{4}}}$ $\phantom{?} = {\dfrac{49}{4}} \times \dfrac{8}{7} ~~~~~~~{\text{Rewrite dividing by} {\dfrac{7}{8}} \text{ as multiplying by} \dfrac{8}{7}}$ $\phantom{?} =\dfrac{49 \times 8}{4 \times 7}$ $\phantom{?} =\dfrac{392}{28}$ $\phantom{?} = {14 \text{ signs}}$ There are $14$ speed limit signs on this stretch of highway.